Self-consistent solution of the second-order Dyson equation for single-particle propagators, with application to the spectral functions of 48Ca

We present a new method to describe the fragmentation of single-particle strength in the framework of the Green function formalism. By means of an iterative scheme, we are able to construct a self-consistent solution of the Dyson equation up to second order in the interaction. Damping effects, such as the broadening of the spectral function for deep-lying hole states, show up in a natural way. We apply the formalism to a schematic model and to the case of the doubly-closed shell nucleus ⁴⁸Ca.